This is extremely helpful and really appreciated. You all have been more helpful than any of the travel companies we've spoken to. I also contacted Heathrow through the website but it was a fairly standard response I got (they recommended using the Heathrow Express and the underground).Hi
Thanks for the replies. So yes that does sound like you are on one booking and therefore when you go to the BA check in desks at EDI they will check your bags on to the DOH flight. When you get to LHR you won't have to see your bags again.
In terms of the connection, it is now under the minimum connection time for a T5 to T4 connection. When time changes happen to a flight they don't always take in to account other flights on the booking, so your EDI-LHR has changed but it won't automatically change anything and notice it is now under the minimum connection time. The danger is at some point the system will pick up on this and cancel your other flight or rebook you on something else. You do need to sort this out before you travel, and I guess the easiest option will be to change to an earlier EDI-LHR flight. As you booked with a travel agent you will have to deal with them unfortunately. However, your change to an earlier EDI flight will be free. Mention to them explicitly that due to the time change you are now under the MCT for the connection and therefore they must rebook you.
In terms of the actual mechanics of the connection, this should be fairly straightforward. You will arrive in to the domestic gates at the north end of T5A. When you step off the jetbridge turn left and follow the purple signs for "Flight Connections T2,3,4" At some point when you walk along a Heathrow airport person will just ask to see your bp just to check you are heading in the correct direction. Once past that keep walking along and around 100m down you will see signs showing you to to go down an escalator on the left for connections to T234. Go down there and get the airside bus to T4. Once at T4 you will go through connection security and once that is done you will be in the airside departures area. From stepping off the plan the process should take around 35-50 minutes.
It's possible you will arrive on a remote stand and be bussed but you will be bussed to the ground floor around the same part of T5A, so just go upstairs when you enter the building (don't go out through the glass doors) and follow the same as above.
The trains thing would only be if on arrival you existed landside and then went across to T4, which you could do but I wouldn't recommend in your case.
Hope this helps.
Once again, many thanks for all the help.